Digital system for estimating signal non-energy parameters using a digital Phase Locked Loop

ABSTRACT

A digital system of measuring parameters of the signal (phase, frequency and frequency derivative) received in additive mixture with Gaussian noise. The system is based on the use of variables of a PLL for calculating preliminary estimates of parameters and calculating the corrections for these estimates when there is a spurt frequency caused by a receiver motion with a jerk. A jerk is determined if the low pass filtered signal of the discriminator exceeds a certain threshold. The jerk-correction decreases the dynamic errors. Another embodiment includes a tracking filter for obtaining preliminary estimates of parameters to reduce the fluctuation errors. Estimates are taken from the tracking filter when there is no jerk and from the block of jerk-corrections when there is a jerk.

BACKGROUND OF THE INVENTION

Phase, frequency and frequency derivative are parameters independent of energy of the input signal (i.e., non-energy parameters). There are known methods of estimating signal non-energy parameters based on processing of variables received from a phase-lock loop (PLL).

U.S. Pat. No. 7,869,554, entitled “Phase/frequency estimator-based phase locked loop”, discloses an apparatus and methods described in use a PLL and provided a phase estimation of the input signal from which signal frequency is estimated by a derivative function and low pass filtering.

U.S. Pat. No. 3,895,294, entitled “Phase change measuring circuit”, discloses a device for measuring the phase change of an input signal over a specified period comprising a phase-locked tracking filter including a high frequency voltage-controlled oscillator (VCO), a frequency divider to give local oscillator signal at the same frequency as the input signal and a counter counting cycles of the VCO whose phase change in any period is N times the input phase change to allow 1/N period resolution, N being an arbitrary integer. The phase change measuring circuit thus allows phase measurement with a resolution within a small fraction of one cycle.

U.S. Pat. No. 7,222,035, entitled “Method and apparatus for determining changing signal frequency”, discloses a method and apparatus which include a PLL having a numerically controlled oscillator (NCO) and a filter of frequency estimates (FFE). The PLL tracks the changing signal frequency and outputs non-smoothed frequency estimates into the FFE. The FFE then smoothes noise in the signal to produce a more accurate smoothed frequency estimate of the input signal.

US Patent Publication No. 20140072084, entitled “Digital system and method of estimating quasi-harmonic signal non-energy parameters using a digital Phase Locked Loop”, discloses a digital system and method of measuring (estimating) non-energy parameters of the signal (phase, frequency and frequency rate) received in additive mixture with Gaussian noise. The first embodiment of the measuring system consists of a PLL system tracking variable signal frequency, a block of NCO full phase computation (OFPC), a block of signal phase preliminary estimation (SPPE) and a first type adaptive filter filtering the signal from the output of SPPE. The second embodiment of the invention has no block SPPE, and NCO full phase is fed to the input of a second type adaptive filter.

A DPLL described in U.S. Pat. No. 4,771,250 generates signal phase which is an approximation of the phase of the received signal with a linear estimator. The effect of a complication associated with non-zero transport delays related to the DPLL is then compensated by a predictor. The estimator provides recursive estimates of phase, frequency, and higher order derivatives, while the predictor compensates for transport lag inherent in the loop.

However, the above references, as well as other conventional methods of measuring non-energy signal parameters using PLL are not adaptive to the jerking motion (when, for example, the acceleration varies linearly in time) of the receiver, or adapt to it by expanding the bandwidths of PLL or using smoothing filters. It is not possible to completely eliminate the dynamic measurement errors using conventional methods.

Unlike the methods above, the present invention enables to obtain accurate phase estimates of the input signal and its derivatives by correcting the preliminary estimates at sites with jerking motion and by an additional filtering of phase estimates at sites without such jerking motion.

The present invention can be used in receivers of various navigation systems, such as GPS, GLONASS and GALILEO, which provide precise measurements of signal phase at different rates of frequency change, as well as systems using digital PLLs for speed measurements.

SUMMARY OF THE INVENTION

Accordingly, the present invention is related to a system of estimating quasi-harmonic signal non-energy parameters using a digital Phase Locked Loop that substantially obviates one or more of the disadvantages of the related art.

In one embodiment, a system for estimating parameters of an input signal includes (a) a digital phase locked loop (PLL) that tracks the input signal and includes:

-   -   i) a phase discriminator (PD) that determines a phase difference         between the input signal and reference signals;     -   ii) a loop filter (LF) with a control period T_(c) operating         based on:

$\left. \begin{matrix} {{\phi_{i}^{LF} = {\alpha^{LF} \cdot z_{i}^{d}}},} \\ {{s_{i}^{\gamma} = {s_{i - 1}^{\gamma} + {\gamma^{LF} \cdot z_{i}^{d}}}},} \\ {{s_{i}^{\beta} = {s_{i - 1}^{\beta} + s_{i}^{\gamma} + {\beta^{LF} \cdot z_{i}^{d}}}},} \\ {{\phi_{i}^{r} = {{round}\left( {\phi^{LF}/\Delta_{\phi}^{NCO}} \right)}},} \\ {{f_{i}^{r} = {{round}\left( {{s_{i}^{\beta}/\Delta_{\omega}^{NCO}}/T_{c}} \right)}},} \end{matrix} \right\},$

-   -   -   where α^(LF), β^(LF), γ^(LF) are constants,         -   z_(i) ^(d) is a PD output;         -   φ_(i) ^(r) is a phase code for a Numerically Controlled             Oscillator (NCO),         -   f_(i) ^(r) is a frequency code for the NCO,         -   Δ_(φ) ^(NCO) is a phase step size in the NCO,         -   Δ_(ω) ^(NCO) is a frequency step size in the NCO, and         -   round (.) is an operation of numerical rounding;

    -   iii) the NCO having frequency and phase control using φ_(i) ^(r)         and f_(i) ^(r),

    -   wherein an output of the NCO is connected to a reference input         of the PD;

-   (b) a calculation of full phase (CFP) block that inputs φ_(i) ^(r)     and f_(i) ^(r) and that operates based on φ_(i) ^(NCO)=φ_(i−1)     ^(NCO)+φ_(i) ^(r)·Δ_(φ) ^(NCO)+f_(i−1) ^(r)·Δ_(ω) ^(NCO)·T_(c); (c)     a low-pass filter (LPF) inputting z_(i) ^(d);     -   a preliminary estimation of signal parameters (PESP) block that         inputs φ_(i) ^(NCO), f_(i) ^(r) and s_(i) ^(γ), outputs a         preliminary estimate for a signal phase {circumflex over         (φ)}_(i) ^(c,E) and a preliminary estimate for a signal         frequency {circumflex over (ω)}_(i) ^(c,E) based on:

{circumflex over (φ)}_(i) ^(c,E)=φ_(i) ^(NCO) +s _(i) ^(γ)/12,

{circumflex over (ω)}_(i) ^(c,E)=2π·f _(i) ^(r) −s _(i) ^(γ)/(2·T _(c));

-   (d) a jerk-corrections of preliminary estimates (JCPE) block     inputting z_(i) ^(A), wherein the JCPE block outputs an estimate for     a signal phase {circumflex over (φ)}_(i) ^(c) and an estimate for a     signal frequency {circumflex over (ω)}_(i) ^(c) based on:

${{\left. {{{\left. \begin{matrix} {{\hat{\phi}}_{i}^{c} = {{\hat{\phi}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\phi}}}} \\ {{\hat{\omega}}_{i}^{c} = {{\hat{\omega}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\omega}}}} \end{matrix} \right\} {\mspace{11mu} \;}{if}\mspace{14mu} z_{i}^{A}} > T_{A}},\begin{matrix} {{{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{C,E}},} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,E}} \end{matrix}} \right\} {\mspace{11mu} \;}{if}\mspace{14mu} z_{i}^{A}} \leq T_{A}},$ C _(φ)=1−α^(LF)/2+β^(LF)/12+γ^(LF)/24,

C _(ω)=(α^(LF)−β^(LF)/2−γ^(LF)/6)/T _(c), and

-   -   T_(A) is a threshold.

Additional features and advantages of the invention will be set forth in the description that follows, and in part will be apparent from the description, or may be learned by practice of the invention. The advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE ATTACHED FIGURES

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention.

In the drawings:

FIG. 1 is a block diagram for a first embodiment of the invention.

FIG. 2 is an example of an arc tangent-type phase discriminator (PD).

FIG. 3 is a block diagram for a second embodiment of the invention.

FIG. 4 illustrates a jerk as a function of time.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

In embodiments of the present invention, adaptation to the nature of the movement of the receiver is made not by changing the parameters of FAP, but by changing the algorithm for estimating the signal parameters. For this purpose, corrections that compensate for the dynamic measurement errors during jerking motion are produced.

FIG. 1 shows a block-diagram of the first embodiment of the invention. The measuring system shown in this figure is based on the use of variables of a PLL for calculating preliminary estimates of non-energy signal parameters (i.e., phase, frequency and frequency derivative (frequency drift)) and calculating the corrections when there is a spurt frequency caused by a receiver's jerking motion. The measuring system comprises a digital PLL (101) that has the following main components: a phase discriminator (PD) (102), loop filter (LF) (103), and numerically-controlled oscillator (NCO) (103) with frequency and phase control. Samples U_(n) ^(mix) of an analog process U^(mix)(t) at a sampling frequency f_(s) are fed to the discriminator input. An analog process U^(mix)(t)=U^(c)(t)+U^(n)(t) representing an additive mixture of quasi-harmonic signal U^(c)(t) and Gaussian noise U^(n)(t). Desired signal U^(c)(t) is equal to U^(c)(t)=A^(c)·cos[φ^(c)(t)],

where A^(c) is the amplitude of the signal,

-   -   φ^(c)(t)=∫ω^(c)(t)·dt+φ₀ is the signal phase [in radians],     -   ω^(c)(t) is the signal frequency [in radian/s],     -   φ₀ is the initial signal phase [in radian].

Signal phase φ^(c)(t), signal frequency ω^(c)(t) and frequency derivative {dot over (ω)}^(c)(t) should be estimated (measured).

A loop filter (LF) operates with a control period T_(c) on the basis of recurrence equations:

$\left. \begin{matrix} {{\phi_{i}^{LF} = {\alpha^{LF} \cdot z_{i}^{d}}},} \\ {{s_{i}^{\gamma} = {s_{i - 1}^{\gamma} + {\gamma^{LF} \cdot z_{i}^{d}}}},} \\ {{s_{i}^{\beta} = {s_{i - 1}^{\beta} + s_{i}^{\gamma} + {\beta^{LF} \cdot z_{i}^{d}}}},} \\ {{\phi_{i}^{r} = {{round}\left( {\phi^{LF}/\Delta_{\phi}^{NCO}} \right)}},} \\ {{f_{i}^{r} = {{round}\left( {{s_{i}^{\beta}/\Delta_{\omega}^{NCO}}/T_{c}} \right)}},} \end{matrix} \right\},$

where α^(LF), β^(LF), γ^(LF) are constant transfer coefficients,

z_(i) ^(d) is the PD output;

φ_(i) ^(r) is the phase code for NCO,

f_(i) ^(r) is the frequency code for NCO,

Δ_(φ) ^(NCO) is the phase step size (radian) in the NCO,

Δ_(ω) ^(NCO) is the frequency step size (radian/s) in the NCO,

round ( ) is the operation of a numerical rounding.

A numerically controlled oscillator (NCO) (104) has frequency and phase control. The phase input of the NCO is connected to the phase output φ_(i) ^(r) of the loop filter (LF) and the frequency input of the NCO is connected to the frequency output f_(i) ^(r) of the LF (103); wherein a complex output of a NCO connected to a reference input of a PD (102).

FIG. 2 shows an example of PD. Input samples U_(n) ^(mix) are multiplied by quadrature samples (I_(n) ^(ref), Q_(n) ^(ref)) from the NCO,

$\left. \begin{matrix} {I_{n}^{ref} = {A^{NCO} \cdot {\cos \left( \phi_{n}^{w,{NCO}} \right)}}} \\ {Q_{n}^{ref} = {A^{NCO} \cdot {\sin \left( \phi_{n}^{w,{NCO}} \right)}}} \end{matrix} \right\},$

where A^(NCO) is the sample amplitude, and φ_(n) ^(w,NCO) is the wrapped phase (i.e., 0≦φ_(n) ^(w,NCO)<+2π) of NCO in radians. Multiplication results

$\left. \quad\begin{matrix} {I_{n}^{mr} = {U_{n}^{mix} \cdot I_{n}^{ref}}} \\ {Q_{n}^{mr} = {U_{n}^{mix} \cdot Q_{n}^{ref}}} \end{matrix} \right\}$

are fed to the input of low-pass filters, which are typically the reset accumulators Σ↓ with frequency F_(c)<<f_(s). The reset frequency of the accumulators F_(c) is the control frequency in the PLL, for example, F_(c)=50 Hz . . . 1000 Hz; f_(s)=10 MHz . . . 100 MHz. The outputs of the reset accumulators are

$I_{i} = {{\sum\limits_{m = 1}^{m = N_{s}}\; {I_{m + {{({i - 1})} \cdot N_{s}}}^{mr}\mspace{14mu} {and}\mspace{14mu} Q_{i}}} = {\sum\limits_{m = 1}^{m = N_{s}}\; {Q_{m + {{({i - 1})} \cdot N_{s}}}^{mr}.}}}$

The output of a phase discriminator is

z _(i) ^(d)=arc tan(Q _(i) /I _(i)) [in radians].

Further, the signal z_(i) ^(d) from the PD output is inputted to the loop filter (LF) (FIG. 2), which operates with a control period T_(c)=N_(s)/f_(s) on the basis of recurrence equation:

$\left. \begin{matrix} {{\phi_{i}^{LF} = {\alpha^{LF} \cdot z_{i}^{d}}},} \\ {{s_{i}^{\gamma} = {s_{i - 1}^{\gamma} + {\gamma^{LF} \cdot z_{i}^{d}}}},} \\ {{s_{i}^{\beta} = {s_{i - 1}^{\beta} + s_{i}^{\gamma} + {\beta^{LF} \cdot z_{i}^{d}}}},} \\ {{\phi_{i}^{r} = {{round}\left( {\phi^{LF}/\Delta_{\phi}^{NCO}} \right)}},} \\ {{f_{i}^{r} = {{round}\left( {{s_{i}^{\beta}/\Delta_{\omega}^{NCO}}/T_{c}} \right)}},} \end{matrix} \right\},$

where α^(LF), β^(LF), γ^(LF) are constant transfer coefficients,

z_(i) ^(d) is the PD output;

φ_(i) ^(r) is the phase code for the NCO,

f_(i) ^(r) is the frequency code for the NCO,

Δ_(φ) ^(NCO) is the phase step size (radian) in the NCO,

Δ_(ω) ^(NCO) is the frequency step size (radian/s) in the NCO, and

round (.) is the operation of a numerical rounding.

Digital phase samples φ_(i) ^(r) are fed to the NCO phase control input and abruptly change its phase by the corresponding value Δφ_(i) ^(NCO)=φ_(i) ^(r)·Δ_(φ) ^(NCO), where Δ_(φ) ^(NCO) is the phase step size. Samples f_(i) ^(r) (frequency codes) are delivered to the NCO frequency input and determine its frequency ω_(i) ^(ref)=f_(i) ^(r)·Δ_(ω) ^(NCO), where Δ_(ω) ^(NCO) is the frequency step size [radian/s] in the NCO.

The measuring system (see FIG. 1) comprises also:

block (105) for calculation of full phase (CFP) of NCO, coupled with the LF outputs, operates on the basis of equation

φ_(i) ^(NCO)=φ_(i−1) ^(NCO)+φ_(i) ^(r)·Δ_(φ) ^(NCO) +f _(i−1) ^(r)·Δ_(ω) ^(NCO) ·T _(c);

block (106)—a low-pass filter (LPF) coupled with an output z_(i) ^(d) of a PD;

block (107)—a block for preliminary estimation of signal parameters (PESP) coupled by its inputs with:

the phase output φ_(i) ^(NCO) of a block for CFP of a NCO,

the frequency output f_(i) ^(r) of the loop filter,

the output s_(i) ^(γ) of the loop filter;

where a block for PESP operates on the basis of equations:

{circumflex over (φ)}_(i) ^(c,E)=φ_(i) ^(NCO) +s _(i) ^(γ)/12,

{circumflex over (ω)}_(i) ^(c,E)=2π·f _(i) ^(r) −s _(i) ^(γ)/(2·T _(c)),

{dot over ({circumflex over (ω)})}_(i) ^(c,E) =s _(i) ^(γ) /T _(c) ²;

where

-   -   {circumflex over (φ)}_(i) ^(c,E) is the preliminary estimate for         a signal phase [in radians],     -   {circumflex over (ω)}_(i) ^(c,E) is the preliminary estimate for         a signal frequency [radian/s],     -   {dot over ({circumflex over (ω)})}_(i) ^(c,E) is the preliminary         estimate for a signal frequency derivative [radian/s²];

block (108) is a threshold unit coupled with an output z_(i) ^(A) of a LPF; where an output J_(i) of a threshold unit is given by the formula:

J_(i)=true, if z_(i) ^(A)>T_(A),

J_(i)=false, if z_(i) ^(A)≦T_(A),

here T_(A) is a threshold; the threshold value is set equal to (3 . . . 5)·RMS(z_(i) ^(A)).

block (109)—a block for jerk-corrections of preliminary estimates (JCPE) coupled with an output z_(i) ^(A) of a LPF and with an output J_(i) of a threshold unit; where the block JCPE operates on the basis of equations:

$\left. {\left. \begin{matrix} {{\hat{\phi}}_{i}^{c} = {{\hat{\phi}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\phi}}}} \\ {{\hat{\omega}}_{i}^{c} = {{\hat{\omega}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\omega}}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {{\hat{\overset{.}{\omega}}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\overset{.}{\omega}}}}} \end{matrix} \right\} {{{{if}\mspace{14mu} J_{i}} = {true}},\begin{matrix} {{{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,E}},} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,E}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i}^{c,E}} \end{matrix}}} \right\}$ if  J_(i) = false,

-   -   where         -   {circumflex over (φ)}_(i) ^(c) is the estimate for a signal             phase [in radians],         -   {circumflex over (ω)}_(i) ^(c) is the estimate for a signal             frequency [in radian/s],         -   {dot over ({circumflex over (ω)})}_(i) ^(c) is the estimate             for a signal frequency derivative [in radian/s²],

C _(φ)=1−α^(LF)/2+β^(LF)/12+γ^(LF)/24,

C _(ω)=(α^(LF)−β^(LF)/2−γ^(LF)/6)T _(c),

C _({dot over (ω)})=β^(LF) /T _(c) ².

FIG. 3 shows a block-diagram of the second embodiment of the invention. The measuring system is based on the use of variables of a PLL for calculating preliminary estimates of signal parameters (phase, frequency and frequency derivative) and calculating the corrections when there is a spurt frequency caused by a receiver jerking motion. When a frequency spurt is absent, the parameter estimates are obtained by 3rd order tracking filter, whose input is fed by a preliminary assessment of phase. The measuring system FIG. 3 comprises blocks (301), (302), (303), (304), (305), (306), (307), (308), (309). All of these blocks and their connection are the same as in the first embodiment respectively (101), (102), (103), (104), (105), (106), (107), (108), (109), except that the output of unit (308) does not feed unit (309).

Block (309) for jerk-corrections of preliminary estimates (JCPE) coupled with an output z_(i) ^(A) of a LPF and operates on the basis of equations:

$\left. \begin{matrix} {{{\hat{\phi}}_{i}^{c,J} = {{\hat{\phi}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\phi}}}},} \\ {{\hat{\omega}}_{i}^{c,J} = {{\hat{\omega}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\omega}}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c,J} = {{\hat{\overset{.}{\omega}}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\overset{.}{\omega}}}}} \end{matrix} \right\},$

where {circumflex over (φ)}_(i) ^(c,J), {circumflex over (ω)}_(i) ^(c,J), {dot over ({circumflex over (ω)})}_(i) ^(c,J) are, respectively, estimates with jerk-corrections for a phase [in radians], frequency [in radian/s] and frequency derivative [radian/s²] of a signal.

Block (309) for jerk-corrections of preliminary estimates (JCPE) reduces dynamic error of estimates due to frequency spurts, but it increases fluctuation errors of estimates. The measuring system, see FIG. 3, comprises a 3rd order tracking filter of phase (TFP) (310) to reduce the fluctuation errors in the absence of frequency spurt; wherein a TFP bandwidth is less than a PLL bandwidth. Block TFP (310) coupled with the outputs {circumflex over (φ)}_(i) ^(c,E) of the PESP, operates on the basis of recurrence equations:

$\left. \begin{matrix} {{\overset{\_}{\phi}}_{i}^{c,T} = {{\hat{\phi}}_{i - 1}^{c,T} + {{\hat{\omega}}_{i - 1}^{c,T} \cdot T_{c}} + {{\hat{\overset{.}{\omega}}}_{i - 1}^{c,T} \cdot {T_{c}^{2}/2}}}} \\ {{\overset{\_}{\omega}}_{i}^{c,T} = {{\hat{\omega}}_{i - 1}^{c,T} + {{\hat{\overset{.}{\omega}}}_{i - 1}^{c,T} \cdot T_{c}}}} \\ {{\overset{\_}{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i - 1}^{c,T}} \end{matrix} \right\}\quad$ z _(i) ^(T)=φ_(i) ^(NCO)−φ _(i) ^(c,T),

$\left. \begin{matrix} {{\hat{\phi}}_{i}^{c,T} = {{\overset{\_}{\phi}}_{i}^{c,T} + {\alpha^{T} \cdot z_{i}^{T}}}} \\ {{\hat{\omega}}_{i}^{c,T} = {{\overset{\_}{\omega}}_{i}^{c,T} + {\beta^{T} \cdot {z_{i}^{T}/T_{c}}}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c,T} = {{\overset{\_}{\overset{.}{\omega}}}_{i}^{c,T} + {\gamma^{T} \cdot {z_{i}^{T}/T_{c}^{2}}}}} \end{matrix} \right\},$

where α^(T), β^(T), γ^(T) are constant transfer coefficients of the TFP.

Block (311) decides on which group of estimates for signal parameters should be taken; this block takes the estimates from the TFP block when there is no jerk, otherwise, it takes the estimates from the JCPE (when there is jerk), i.e.

$\left. {\left. \begin{matrix} {{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,T}} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,T}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i}^{c,T}} \end{matrix} \right\} {{{{if}\mspace{14mu} J_{i}} = {false}},\begin{matrix} {{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,J}} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,J}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i}^{c,J}} \end{matrix}}} \right\}$ if  J_(i) = true;

where

{circumflex over (φ)}_(i) ^(c) is the estimate for a signal phase [in radians],

{circumflex over (ω)}_(i) ^(c) is the estimate for a signal frequency [in radian/s],

{dot over ({circumflex over (ω)})}_(i) ^(c) is the estimate for a signal frequency derivative [in radian/s²].

FIG. 4 shows an example of motion with jerks. This jerking motion consists of: 0<t≦t₁ and t>t₄ are states without movement, t₁<t≦t₂ and t₃<t≦t₄ are states with jerks, when the acceleration varies linearly, t₂<t≦t₃ is the state with a constant acceleration.

Having thus described a preferred embodiment, it should be apparent to those skilled in the art that certain advantages of the described apparatus have been achieved.

It should also be appreciated that various modifications, adaptations, and alternative embodiments thereof may be made within the scope and spirit of the present invention. The invention is further defined by the following claims. 

What is claimed is:
 1. A system for estimating non-energy parameters of an input signal, the system comprising: a) a third order digital phase locked loop (PLL) that tracks the input signal and includes: i) a phase discriminator (PD), whose signal input receives a discretized input signal, wherein the PD determines a phase difference between the input signal and reference signals; ii) a loop filter (LF) with a control period T_(c) operating based on equation: $\left. \begin{matrix} {{\phi_{i}^{LF} = {\alpha^{LF} \cdot z_{i}^{d}}},} \\ {{s_{i}^{\gamma} = {s_{i - 1}^{\gamma} + {\gamma^{LF} \cdot z_{i}^{d}}}},} \\ {{s_{i}^{\beta} = {s_{i - 1}^{\beta} + s_{i}^{\gamma} + {\beta^{LF} \cdot z_{i}^{d}}}},} \\ {{\phi_{i}^{r} = {{round}\left( {\phi^{LF}/\Delta_{\phi}^{NCO}} \right)}},} \\ {{f_{i}^{r} = {{round}\left( {{s_{i}^{\beta}/\Delta_{\omega}^{NCO}}/T_{c}} \right)}},} \end{matrix} \right\},$ where α^(LF), β^(LF), γ^(LF) are constant transfer coefficients, z_(i) ^(d) is a PD output; φ_(i) ^(r) is a phase code for a Numerically Controlled Oscillator (NCO), f_(i) ^(r) is a frequency code for the NCO, Δ_(φ) ^(NCO) is a phase step size in the NCO, Δ_(ω) ^(NCO) is a frequency step size in the NCO, and round (.) is an operation of numerical rounding; iii) the NCO having frequency and phase control, and whose phase input is connected to the phase output φ_(i) ^(r) and whose frequency input is connected to the frequency output f_(i) ^(r), wherein a complex output of the NCO is connected to a reference input of the PD; b) a block for calculation of full phase (CFP) of the NCO, inputting the LF outputs, and operating based on equation φ_(i) ^(NCO)=φ_(i−1) ^(NCO)+φ_(i) ^(r)·Δ_(φ) ^(NCO) +f _(i−1) ^(r)·Δ_(ω) ^(NCO) ·T _(c); c) a low-pass filter (LPF) inputting the output z_(i) ^(d); d) a block for preliminary estimation of signal parameters (PESP) inputting: the phase output φ_(i) ^(NCO), the frequency output f_(i) ^(r), the output s_(i) ^(γ), wherein the block for PESP operates based on: {circumflex over (φ)}_(i) ^(c,E)=φ_(i) ^(NCO) +s _(i) ^(γ)/12, {circumflex over (ω)}_(i) ^(c,E)=2π·f _(i) ^(r) −s _(i) ^(γ)/(2·T _(c)), {dot over ({circumflex over (ω)})}_(i) ^(c,E) =s _(i) ^(γ) /T _(c) ²; where {circumflex over (φ)}_(i) ^(c,E) is a preliminary estimate for a signal phase, {circumflex over (ω)}_(i) ^(c,E) is a preliminary estimate for a signal frequency, {dot over ({circumflex over (ω)})}_(i) ^(c,E) is a preliminary estimate for a signal frequency derivative; e) a threshold unit inputting the output z_(i) ^(A), wherein an output J_(i) of the threshold unit is given by J_(i)=true, if z_(i) ^(A)>T_(A), J_(i)=false, if z_(i) ^(A)≦T_(A), where T_(A) is a threshold; f) a block for jerk-corrections of preliminary estimates (JCPE) inputting the output z_(i) ^(A) and the output J_(i), wherein the block JCPE operates based on: $\left. {\left. \begin{matrix} {{\hat{\phi}}_{i}^{c} = {{\hat{\phi}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\phi}}}} \\ {{\hat{\omega}}_{i}^{c} = {{\hat{\omega}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\omega}}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {{\hat{\overset{.}{\omega}}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\overset{.}{\omega}}}}} \end{matrix} \right\} {{{{if}\mspace{14mu} J_{i}} = {true}},\begin{matrix} {{{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,E}},} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,E}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i}^{c,E}} \end{matrix}}} \right\}$ if  J_(i) = false, where {circumflex over (φ)}_(i) ^(c) is an estimate for a signal phase, {circumflex over (ω)}_(i) ^(c) is an estimate for a signal frequency, {dot over ({circumflex over (ω)})}_(i) ^(c) is an estimate for a signal frequency derivative, C _(φ)=1−α^(LF)/2+β^(LF)/12+γ^(LF)/24, C _(ω)=(α^(LF)−β^(LF)/2−γ^(LF)/6)/T _(c), C _({dot over (ω)})=β^(LF) /T _(c) ².
 2. The system of claim 1, wherein the LPF operates based on z _(i) ^(A) =z _(i−1) ^(A)+α^(LPF)·(z _(i) ^(d) −z _(i−1) ^(A)), where α^(LPF) is a constant transfer coefficient, 0<α^(LPF)<1.
 3. A system for estimating non-energy parameters of an input signal, the system comprising: a) a third order digital phase locked loop (PLL) that tracks the input signal and includes: (i) a phase discriminator (PD), whose signal input is a discretized input signal, wherein the PD determines a phase difference between the input signal and reference signals; (ii) a loop filter (LF) with a control period based on equations: $\left. \begin{matrix} {{\phi_{i}^{LF} = {\alpha^{LF} \cdot z_{i}^{d}}},} \\ {{s_{i}^{\gamma} = {s_{i - 1}^{\gamma} + {\gamma^{LF} \cdot z_{i}^{d}}}},} \\ {{s_{i}^{\beta} = {s_{i - 1}^{\beta} + s_{i}^{\gamma} + {\beta^{LF} \cdot z_{i}^{d}}}},} \\ {{\phi_{i}^{r} = {{round}\left( {\phi^{LF}/\Delta_{\phi}^{NCO}} \right)}},} \\ {{f_{i}^{r} = {{round}\left( {{s_{i}^{\beta}/\Delta_{\omega}^{NCO}}/T_{c}} \right)}},} \end{matrix} \right\},$ where α^(LF), β^(LF), γ^(LF) are constant transfer coefficients, z_(i) ^(d) is a PD output; φ_(i) ^(r) is a phase code for a numerically controlled oscillator (NCO), f_(i) ^(r) is a frequency code for the NCO, Δ_(φ) ^(NCO) is a phase step size in the NCO, Δ_(ω) ^(NCO) is a frequency step size in the NCO, round (.)—a operation of a numerical rounding; and (iii) the NCO having frequency and phase control, whose phase input is connected to the phase output φ_(i) ^(r) and a frequency input is connected to the frequency output f_(i) ^(r), wherein a complex output of the NCO is connected to a reference input of the PD; b) a block for calculation of full phase (CFP) of the NCO, inputting the LF outputs, and operating based on equation φ_(i) ^(NCO)=φ_(i−1) ^(NCO)+φ_(i) ^(r)·Δ_(φ) ^(NCO) +f _(i−1) ^(r)·Δ_(ω) ^(NCO) ·T _(c); c) a low-pass filter (LPF) inputting the output z_(i) ^(d); d) a block for preliminary estimation of signal parameters (PESP) having as its inputs the phase output φ_(i) ^(NCO), the frequency output f_(i) ^(r), and the output s_(i) ^(γ); wherein a block for PESP operates based on equation: $\left. \begin{matrix} {{\hat{\phi}}_{i}^{c,E} = {\phi_{i}^{NCO} + {s_{i}^{\gamma}/12}}} \\ {{\hat{\omega}}_{i}^{c,E} = {{2{\pi \cdot f_{i}^{NCO}}} - {s_{i}^{\gamma}/\left( {2 \cdot T_{c}} \right)}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c,E} = {s_{i}^{\gamma}/T_{c}^{2}}} \end{matrix} \right\}\quad$ where {circumflex over (φ)}_(i) ^(c,E) is a preliminary estimate for a signal phase, {circumflex over (ω)}_(i) ^(c,E) is a preliminary estimate for a signal frequency, {dot over ({circumflex over (ω)})}_(i) ^(c,E) is a preliminary estimate for a signal frequency derivative; e) a threshold unit inputting the output z_(i) ^(A) of the LPF, wherein an output J_(i) of the threshold unit is given by: J_(i)=true, if z_(i) ^(A)>T_(A), J_(i)=false, if z_(i) ^(A)≦T_(A), where T_(A) is a threshold; f) a block for jerk-corrections of preliminary estimates (JCPE) receiving the output z_(i) ^(A) of a LPF and operating based on equations: $\left. \begin{matrix} {{{\hat{\phi}}_{i}^{c,J} = {{\hat{\phi}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\phi}}}},} \\ {{\hat{\omega}}_{i}^{c,J} = {{\hat{\omega}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\omega}}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c,J} = {{\hat{\overset{.}{\omega}}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\overset{.}{\omega}}}}} \end{matrix} \right\},$ where {circumflex over (φ)}_(i) ^(c,J), {circumflex over (ω)}_(i) ^(c,J), {dot over ({circumflex over (ω)})}_(i) ^(c,J) are, respectively, estimates with jerk-corrections for a phase, frequency and frequency derivative of the input signal; C _(φ)=1−α^(LF)/2+β^(LF)/12+γ^(LF)/24, C _(ω)=(α^(LF)−β^(LF)/2−γ^(LF)/6)/T _(c), C _({dot over (ω)})=β^(LF) /T _(c) ²; g) a third order tracking filter of phase (TFP), inputting the output {circumflex over (φ)}_(i) ^(c,E) of the PESP, operates based on equations: $\left. \begin{matrix} {{\overset{\_}{\phi}}_{i}^{c,T} = {{\hat{\phi}}_{i - 1}^{c,T} + {{\hat{\omega}}_{i - 1}^{c,T} \cdot T_{c}} + {{\hat{\overset{.}{\omega}}}_{i - 1}^{c,T} \cdot {T_{c}^{2}/2}}}} \\ {{\overset{\_}{\omega}}_{i}^{c,T} = {{\hat{\omega}}_{i - 1}^{c,T} + {{\hat{\overset{.}{\omega}}}_{i - 1}^{c,T} \cdot T_{c}}}} \\ {{\overset{\_}{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i - 1}^{c,T}} \end{matrix} \right\}\quad$ z _(i) ^(T)=φ_(i) ^(NCO)−φ _(i) ^(c,T), $\left. \begin{matrix} {{\hat{\phi}}_{i}^{c,T} = {{\overset{\_}{\phi}}_{i}^{c,T} + {\alpha^{T} \cdot z_{i}^{T}}}} \\ {{\hat{\omega}}_{i}^{c,T} = {{\overset{\_}{\omega}}_{i}^{c,T} + {\beta^{T} \cdot {z_{i}^{T}/T_{c}}}}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c,T} = {{\overset{\_}{\overset{.}{\omega}}}_{i}^{c,T} + {\gamma^{T} \cdot {z_{i}^{T}/T_{c}^{2}}}}} \end{matrix} \right\},$ where α^(T), β^(T), γ^(T) are constant transfer coefficients of the TFP; h) a block for decision of estimates (DE) that takes the estimates from the TFP as the estimates of signal parameters when there is no jerk and takes the estimates from the JCIE block when there is jerk, such that $\left. {\left. \begin{matrix} {{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,T}} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,T}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i}^{c,T}} \end{matrix} \right\} {{{{if}\mspace{14mu} J_{i}} = {false}},\begin{matrix} {{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,J}} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,J}} \\ {{\hat{\overset{.}{\omega}}}_{i}^{c} = {\hat{\overset{.}{\omega}}}_{i}^{c,J}} \end{matrix}}} \right\}$ if  J_(i) = true; where {circumflex over (φ)}_(i) ^(c) is an estimate for a signal phase, {circumflex over (ω)}_(i) ^(c) is an estimate for a signal frequency, and {dot over ({circumflex over (ω)})}_(i) ^(c) is an estimate for a signal frequency derivative.
 4. The system of claim 3, wherein a low-pass filter (LPF) is based on equation z _(i) ^(A) =z _(i−1) ^(A)+α^(LPF)·(z _(i) ^(d) −z _(i−1) ^(A)), where α^(LPF) is a constant transfer coefficient, 0<α^(LPF)<1.
 5. A system for estimating parameters of an input signal, the system comprising: (a) a digital phase locked loop (PLL) that tracks the input signal and includes: (i) a phase discriminator (PD) that determines a phase difference between the input signal and reference signals; (ii) a loop filter (LF) with a control period T_(c) operating based on: $\left. \begin{matrix} {{\phi_{i}^{LF} = {\alpha^{LF} \cdot z_{i}^{d}}},} \\ {{s_{i}^{\gamma} = {s_{i - 1}^{\gamma} + {\gamma^{LF} \cdot z_{i}^{d}}}},} \\ {{s_{i}^{\beta} = {s_{i - 1}^{\beta} + s_{i}^{\gamma} + {\beta^{LF} \cdot z_{i}^{d}}}},} \\ {{\phi_{i}^{r} = {{round}\left( {\phi^{LF}/\Delta_{\phi}^{NCO}} \right)}},} \\ {{f_{i}^{r} = {{round}\left( {{s_{i}^{\beta}/\Delta_{\omega}^{NCO}}/T_{c}} \right)}},} \end{matrix} \right\},$ where α^(LF), β^(LF), γ^(LF) are constants, z_(i) ^(d) is a PD output; φ_(i) ^(r) is a phase code for a Numerically Controlled Oscillator (NCO), f_(i) ^(r) is a frequency code for the NCO, Δ_(φ) ^(NCO) is a phase step size in the NCO, Δ_(ω) ^(NCO) is a frequency step size in the NCO, and round (.) is an operation of numerical rounding; (iii) the NCO having frequency and phase control using φ_(i) ^(r) and f_(i) ^(r), wherein an output of the NCO is connected to a reference input of the PD; (b) a calculation of full phase (CFP) block that inputs φ_(i) ^(r) and f_(i) ^(r) and that operates based on φ_(i) ^(NCO)=φ_(i−1) ^(NCO)+φ_(i) ^(r)·Δ_(φ) ^(NCO)+f_(i−1) ^(r)·Δ_(ω) ^(NCO)·T_(c); (c) a low-pass filter (LPF) inputting z_(i) ^(d); a preliminary estimation of signal parameters (PESP) block that inputs φ_(i) ^(NCO), f_(i) ^(r) and s_(i) ^(γ), and outputs a preliminary estimate for a signal phase {circumflex over (φ)}_(i) ^(c,E) and a preliminary estimate for a signal frequency {circumflex over (ω)}_(i) ^(c,E) based on: {circumflex over (φ)}_(i) ^(c,E)=φ_(i) ^(NCO) +s _(i) ^(γ)/12, {circumflex over (ω)}_(i) ^(c,E)=2π·f _(i) ^(r) −s _(i) ^(γ)/(2·T _(c)); (d) a jerk-corrections of preliminary estimates (JCPE) block inputting z_(i) ^(A), wherein the JCPE block outputs an estimate for a signal phase {circumflex over (φ)}_(i) ^(c) and an estimate for a signal frequency {circumflex over (ω)}_(i) ^(c) based on: $\left. {\left. \begin{matrix} {{\hat{\phi}}_{i}^{c} = {{\hat{\phi}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\phi}}}} \\ {{\hat{\omega}}_{i}^{c} = {{\hat{\omega}}_{i}^{c,E} + {z_{i}^{A} \cdot C_{\omega}}}} \end{matrix} \right\} {if}\; {{z_{i}^{A} > T_{A}},\begin{matrix} {{{\hat{\phi}}_{i}^{c} = {\hat{\phi}}_{i}^{c,E}},} \\ {{\hat{\omega}}_{i}^{c} = {\hat{\omega}}_{i}^{c,E}} \end{matrix}}} \right\}$ if z_(i)^(A) ≤ T_(A), where C _(φ)=1−α^(LF)/2+β^(LF)/12+γ^(LF)/24, C _(ω)=(α^(LF)−β^(LF)/2−γ^(LF)/6)/T _(c), and T_(A) is a threshold.
 6. The system of claim 5, wherein the PD is an arc tangent-type PD.
 7. The system of claim 5, wherein the PLL is a third order PLL.
 8. The system of claim 5, wherein the system also estimates a signal frequency derivative {dot over ({circumflex over (ω)})}_(i) ^(c) as follows: the PESP block outputs a preliminary estimate for a signal frequency derivative {dot over ({circumflex over (ω)})}_(i) ^(c,E)=s_(i) ^(γ)/T_(c) ²; and the JCPE outputs {dot over ({circumflex over (ω)})}_(i) ^(c)={dot over ({circumflex over (ω)})}_(i) ^(c,E) +z _(i) ^(A) ·C _(ω), if z _(i) ^(A) >T _(A), {dot over ({circumflex over (ω)})}_(i) ^(c)={dot over ({circumflex over (ω)})}_(i) ^(c,E), if z_(i) ^(A)≦T_(A), where C _({dot over (ω)})=β^(LF) /T _(c) ².
 9. The system of claim 5, where α^(LF), β^(LF), γ^(LF) are constant transfer coefficients. 